Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/2723 2021 2021 Faculty of Science, Mutah University, Jordan Rashel Rashel Mustansiriah University, Department of Mathematics, Iraq Murhaf Obaidi The main goal of this work is to study the solutions of linear congruencies in the standard and n-standard fuzzy number theoretical systems, where we present necessary and sufficient conditions for fuzzy congruence to be solvable in these systems. Also, we provide the conditions of fuzzy nilpotency and fuzzy invertibility modulo integers with many illustrated examples. On the other hand, we suggest an algorithm to generate fuzzy Pythagoras triples and fuzzy Pythagoras quadruples in the standard fuzzy number theoretical system. 2024 2024 18 22 10.54216/JNFS.080102 https://www.americaspg.com/articleinfo/24/show/2723